Question

In triangle ABC, where angle C is a right angle and CD is the altitude of AB, find the angles in triangle CBD and CAD if angle A = 65 degrees?

Answer 1

In triangle ABC with right angle C and altitude CD, the angles in triangle CBD are 65° and 25°, and the angles in triangle CAD are 25° and 65°.

Step-by-step explanation:

The question involves finding the angles in triangles CBD and CAD within a right-angled triangle ABC where angle C is a right angle, CD is the altitude to AB, and angle A is 65 degrees.

Triangle CAD is a right-angled triangle, so:

Angle A = 65°

Angle C = 90° (as given)

Angle D in triangle CAD can be calculated as: 180° - 90° - 65° = 25°

Now, looking at triangle CBD:

Angle C = 90°

Angle D in triangle CBD is identical to angle D in triangle CAD, so Angle D = 25°

Angle B in triangle CBD can be calculated as: 180° - 90° - 25° = 65°

Therefore, the angles in triangle CBD are 65° and 25°, and the angles in triangle CAD are 25° and 65°.

Answer 2

Angles in triangle CBD are 25 degrees for angle CBD and 65 degrees for angle BDC. In triangle CAD, the angles are 65 degrees for angle CAD and 25 degrees for angle ADC.

Step-by-step explanation:

To find the angles in triangles CBD and CAD when angle A is 65 degrees, and angle C is a right angle, we can use the fact that the sum of the angles in a triangle equals 180 degrees.

• Since angle A is 65 degrees and angle C is a right angle (90 degrees), angle B in triangle ABC is 180 - 65 - 90 = 25 degrees.
• Triangle ABC is a right-angled triangle, so the altitude CD creates two right triangles, CBD and CAD.
• In right triangle CBD, we have a right angle at C, therefore angle CBD is also 25 degrees, because it corresponds to angle B of triangle ABC, and angle BDC is 90 - 25 = 65 degrees.
• In right triangle CAD, angle CAD is already given as 65 degrees, and angle ACD is 90 degrees since CD is the altitude, so angle ADC is 180 - 65 - 90 = 25 degrees.

Therefore, the angles in triangle CBD are 25 degrees for angle CBD and 65 degrees for angle BDC. In triangle CAD, the angles are 65 degrees for angle CAD and 25 degrees for angle ADC.